left In keeping with his democratic ideals, Mackenzie refused the offer of a knighthood three times, and was thus the only one of Canada's first eight Prime Ministers not to be knighted.

A two-sided ideal is a left ideal that is also a right ideal, and is often called an ideal except to emphasize that there might exist single-sided ideals.

These squats had Marxist-Leninist ( but also Stalinist and Maoist ) ideals and come from the left wing of Autonomia.

Spinor spaces were represented as left ideals of a matrix algebra in 1930, by G. Juvet and by Fritz Sauter.

One approach seeks to identify the minimal ideals for the left action of Cℓ ( V, g ) on itself.

In noncommutative ring theory, a maximal right ideal is defined analogously as being a maximal element in the poset of proper right ideals, and similarly, a maximal left ideal is defined to be a maximal element of the poset of proper left ideals.

Maximal right / left / two-sided ideals are the dual notion to that of minimal ideals.

* An important ideal of the ring called the Jacobson radical can be defined using maximal right ( or maximal left ) ideals.

Incidentally this shows that a collection of representatives of simple left R modules is actually a set since it can be put into correspondence with part of the set of maximal left ideals of R.

A radical ring, i. e. a ring in which the Jacobson radical is the entire ring, has no simple modules and hence has no maximal right or left ideals.

* A ring is left-Noetherian if it satisfies the ascending chain condition on left ideals.

* Every non-empty set of left ideals of R, partially ordered by inclusion, has a maximal element with respect to set inclusion.

* Green Left ( GroenLinks ) combines, as its name implies green environmentalist ideals with left ( socialist ) leanings.

His first few pamphlets addressed what he saw as the communist betrayal of left wing ideals, although after the Soviet Union was invaded by Nazi Germany in 1941 he founded the Anglo-Soviet Public Relations Association ( ASPRA ) to promote cordial relations between the UK and Russia.

To the French left, especially socialists and communists, the wall became the symbol of the people's struggle for their liberty and ideals.

Latrobe left Washington with pessimism, with the city's design contradicting many of his ideals.

The fourth property can be paraphrased as follows: a ring R is local if and only if there do not exist two coprime proper ( principal ) ( left ) ideals where two ideals I < sub > 1 </ sub >, I < sub > 2 </ sub > are called coprime if R = I < sub > 1 </ sub > + I < sub > 2 </ sub >.

Letters with asterisks are shown from the side (* L left or * R right ), rather than as the viewer would see them.

Alternative WD1770 / DFS Interfaces such as the P. R. E. S AP4 left & PAGE at E00h.

Let P be the root of the unbalanced subtree, with R and L denoting the right and left children of P respectively.

* If the balance factor of P is-2 then the right subtree outweighs the left subtree of the given node, and the balance factor of the right child ( R ) must be checked.

* If the balance factor of R is-1, a single left rotation ( with P as the root ) is needed ( Right-Right case ).

Abbahu left behind him a number of disciples, the most prominent among whom were the leaders of the 4th amoraic generation, R. Jonah and R. Jose.

For the case of a non-commutative base ring R and a right module M < sub > R </ sub > and a left module < sub > R </ sub > N, we can define a bilinear map, where T is an abelian group, such that for any n in N, is a group homomorphism, and for any m in M, is a group homomorphism too, and which also satisfies

Young ( far left ) with ( L to R ) Jake Stahl, Bill Carrigan and Michael T. McGreevy during spring training in 1912.

The voltage source V on the left drives a Current ( electricity ) | current I around the circuit, delivering electrical energy into the resistor R. From the resistor, the current returns to the source, completing the circuit.

An idempotent element a of R and its associated involution f gives rise to two involutions of the module R, depending on viewing R as a left or right module.

If r represents an arbitrary element of R, f can be viewed as a right R-homomorphism so that, or f can also be viewed as a left R module homomorphism, where.

Raya DunayevskayaThe Johnson – Forest tendency, sometimes called the Johnsonites, refers to a radical left tendency in the United States associated with Marxist theorists C. L. R.

# Only the P < sub > RM </ sub > and P < sub > R '</ sub > promoters are left active, the former producing cI protein and the latter a short inactive transcript.

In March 1982, at the urging of Bad Brains ' H. R., Preslar left college to re-form Minor Threat.

* is a partial function called the transition function, where L is left shift, R is right shift.

In four descending columns, from left to right: Maestrale class frigate | MM Maestrale ( F 570 ), FS De Grasse | De Grasse ( D 612 ); USS John C. Stennis | USS John C. Stennis ( CVN 74 ), FS Charles de Gaulle | Charles De Gaulle ( R 91 ), Surcouf ( F711 ) | Surcouf ( F 711 ); USS Port Royal ( CG-73 ) | USS Port Royal ( CG-73 ), HMS Ocean ( L12 ) | HMS Ocean ( L 12 ), USS John F. Kennedy ( CV 67 ) | USS John F. Kennedy ( CV 67 ), Hr.

While factorially distinct from Eysenck's previous R factor, the S-factor did positively correlate with the R-factor, indicating that a basic left – right or right – left tendency underlies both social values and economic values, although S tapped more into items discussing economic inequality and big business, while R relates more to the treatment of criminals, and to sexual issues and military issues.

They are huge areas which have been swept by winds for so many centuries that there is no soil left, but only deep bare ridges fifty or sixty yards apart with ravines between them thirty or forty feet deep and the only thing that moves is a scuttling layer of sand.

These my grandmother left in their places ( they are still there, more persistent and longer-lived than the generations of man ) and planted others like them, that flourished without careful tending.

He is a widower, his three children are dead, he has no one left on earth ; ;

Well, after everybody has followed the New England pattern of segregating one's children into private schools, only the poor folks are left.

Some brilliant rookies nailed them down, so that this spring just two spots, left and right field, are really up for grabs.

If any are left, presently, we may expect to see signs specifically prohibiting the feeding of them too.

We are left to choose between the two Lindemanns.

When more than two figures are separated by subtraction symbols the subtraction must be carried out from the left to right if the result is to be correct.

It truly relives another age for the inhabitants use carriages rather than autos and old British and French forts are left intact for tourists to visit and record.

There are few areas left where a builder cannot find a dealer equipped to save him money by delivering everything at lower cost just where his workmen will need it.

What we have left as reasonably comparable are four classes: ( 1 ) body parts and products, which with a proportionally nearly even representation ( 51 terms out of 253, 25 out of 100 ) come out with nearly even ratios ; ;

Without such uncertainty we are left with a set of dogmas and myths.

Reefs are left high and dry, and the beaches are covered with stranded fish.

With the loss of the Emperor diety in Japan, the people are left in confusion with no God or moral teachings that have strength.

He said `` Morris County is rapidly changing and unless steps are taken to preserve the green areas, there will be no land left to preserve ''.

We are left helpless to cope with it because we do not dare speak of it as anything real for fear that to do so would imply a commitment to that which has already been discredited and proved false.

There is only one escape left, a tragic one, and too many people are taking it: suicide.

Pope Pius the Sixth, at Rome, in April, 1778, wrote the following: `` The faithful should be excited to the reading of the Holy Scriptures: For these are the most abundant sources which ought to be left open to everyone, to draw from them purity of morals and of doctrine, to eradicate errors which are so widely disseminated in these corrupt times ''.

Only too often, however, you have the feeling that you are sitting in a room with some of the instruments lined up on one wall to your left and others facing them on the wall to your right.

There are times when one suspects that the songs that are dropped from musical shows before they reach Broadway may really be better than many of those that are left in.

New galaxies are forever being formed to fill in the gaps left by the receding galaxies.